Alex is building a rectangular garden in his backyard. The length of the garden is twice its width. If the perimeter of the garden is 48 meters, what is the area of the garden in square meters?

Let the width of the garden be denoted by $w$. Then the length, $l$, can be expressed as $l = 2w$. The formula for the perimeter $P$ of a rectangle is given by:

$$ P = 2(l + w) $$

Using the given perimeter, we can set up the following equation:

$$ 48 = 2(2w + w) $$